3.2-3.4v @ 25ma is the rating for the LED's, if I were to string 36 of them in series, that makes 118v give or take. Unless I misunderstand, all I would need then is a current limiting resistor (56 ohms by my calculator) per string of 36 LED's. This also works out conveniently to just about three watts exactly per string, including the dissipation from the resistor.

One more consideration - The voltage across the LED's is approximately constant. That means the less voltage you drop across the resistor, the worse your "brightness regulation". With 50V across the resistor, a 10% change in the 170V peak voltage is 17V. That entire change appears across the resistor, which means a 34% change in current (and brightness). So with an unregulated power supply, don't try to stack-up as many LEDs as possible in order to minimize the voltage across (and power wasted in) the resistor.

So with an unregulated power supply, don't try to stack-up as many LEDs as possible in order to minimize the voltage across (and power wasted in) the resistor.

I would suggest that that advice be taken together with consideration for efficiency. You want the led string to have a combined forward drop as close to the main's voltage to maximize proficiency. However, that creates bigger current variability when the mains fluctuates.

There are two problems with this approach. First is safety which is covered, second is longevity. Connecting LEDs to the mains is a very bad idea without any type of regulation. LEDs, especially anything using a blue die (Blue, white, pink, purple, sometimes green) or a UV die like you are using are very sensitive to surges and even to static electricity. When you connect to the mains without regulation (using a transformer or not) every surge is going to be passed through to your LEDs. You are proposing a Mains circuit to a rectifier (hopefully through a fuse and preferably an Isolation transformer if the wiring is exposed) to a resistor and then to the LEDs. This leads to problems.